Solve the system of linear equations: \( x-y=2 \) \( 6 x+4 y=92 \) \( x=\square \) \( y=\square \)

To solve the system of equations, let's first rewrite the equations clearly: 1) \( x - y = 2 \) 2) \( 6x + 4y = 92 \) From the first equation, we can express \( x \) in terms of \( y \): \( x = y + 2 \). Now, we substitute \( x \) in the second equation: \( 6(y + 2) + 4y = 92 \). Distributing the \( 6 \): \( 6y + 12 + 4y = 92 \). Combining like terms gives: \( 10y + 12 = 92 \). Subtract \( 12 \) from both sides: \( 10y = 80 \). Dividing by \( 10 \): \( y = 8 \). Now, substitute \( y \) back into the equation for \( x \): \( x = 8 + 2 = 10 \). Thus, the solution is: \( x = 10 \) and \( y = 8 \).